Reference Limits for Outlier Analyses in Randomized Clinical Trials
Charles M. BeasleyBrenda CroweMary NilssonLieLing WuRebeka TabbeyRyan T. HietpasRobert A. DeanPaul S. Horn
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The coverage performance of the confidence intervals (CIs) for the Root Mean Square Standardized Effect Size (RMSSE) was investigated in a balanced, one-way, fixed-effects, between-subjects ANOVA design. The noncentral F distribution-based and the percentile bootstrap CI construction methods were compared. The results indicated that the coverage probabilities of the CIs for RMSSE were not adequate.
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The increase in the squared multiple correlation coefficient (ΔR 2 ) associated with a variable in a regression equation is a commonly used measure of importance in regression analysis. Algina, Keselman, and Penfield found that intervals based on asymptotic principles were typically very inaccurate, even though the sample size was quite large (i.e., larger than 200). However, they also reported that probability coverage for the confidence intervals based on a bootstrap method was typically quite accurate, and moreover, this accuracy was obtained with relatively small sample sizes with six or fewer predictors. They further speculated that nonnormality would likely affect the accuracy of interval coverage. In the present study, the authors investigated the accuracy of coverage probability for confidence intervals obtained by using asymptotic and percentile bootstrap methodology when either predictors, residuals, or both are nonnormal. Coverage probability for asymptotic confidence intervals is poor, but adequate coverage probability can be obtained with reasonable sample sizes by using percentile bootstrap methodology. As well, the authors found that the width of these intervals was relatively precise (i.e., narrow) for the larger cases of sample size investigated.
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Robust confidence intervals
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We construct bootstrap confidence intervals for reliability, R= P{X>Y}, where X and Y are independent normal random variables. One way ANOVA random effect models are assumed for the populations of X and Y, where standard deviations and are unequal. We investigate the accuracy of the proposed bootstrap confidence intervals and classical confidence intervals work better than classical confidence interval for small sample and/or large value of R.
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In metrology, one is usually comparing what indicates an instrument versus what it should be indicated by a reference pattern, resulting in the so called measurement errors. Most errors follow a normal distribution. If one wants to have some confidence about how small is such an error, the traditional confidence intervals for the unknown parameters are computed. This article illustrates, via simulation, the effectiveness of three intervals for estimating the 100p-th percentile in a normal distribution, namely, the Traditional (T), the Normal Asymptotic (NA), and the Lawless (LA) intervals. Various samples of different sizes are drawn from a zero mean normal distribution, which resembles the measurement error distributions. For each one of them the 95% confidence interval is estimated by using the three approaches. From the simulation, it is possible to conclude that T and LA intervals are better than NA as they produce shorter length and wider coverage.
Robust confidence intervals
Confidence distribution
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Absolute deviation
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The Bitterlich Sampling (horizontal point sampling) is a common method in forest inventories. By this method, the Horvitz-Thompson estimator is used in a number of independent sampling points for the estimation of overall tree volume in a forest area/stand. In this paper, confidence intervals are constructed and evaluated using the normal approach and two bootstrap methods; the percentile method (Cα) and the bias-corrected and accelerated method (BCα). The simulation results show that the normal confidence interval has better coverage of true value at sample size 10. At sample sizes 20 and 30, it seems that there are no substantial differences in coverage between confidence intervals, although it could be noted a small superiority of BCα method. At sample size 40, the coverage of the three confidence intervals is higher than the nominal coverage (95%).
Robust confidence intervals
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Abstract In structural timber tests, unintended failure mechanisms occur frequently in specimens and their results are called censored data. There are two censored data analysis: censored maximum likelihood estimation (CMLE) and Kaplan–Meier (KM) method. In this study, the precision of the censored data analysis was investigated to determine the characteristic value, 5th percentile value, of the structural timber. The results show that (1) the 5th percentile value was underestimated by ordinary data analysis methods; maximum likelihood estimation (MLE) and Order statistics. (2) CMLE with 30% lower tail censored data and KM method provided much more precise 5th percentile value. (3) The amount of under-measurement (5 MPa, 10 MPa, and 15 MPa in this simulation study) did not show significant effect on the 5th percentile determination in CMLE and KM method, but the proportion of censored data (percentage of unintended failure specimen; 10%, 20%, 30%, and 40%) affected the determination of 5th percentile value. (4) CMLE with 30% lower tail censored data and KM method showed good agreement in case that the data included unintended failure data up to 20%.
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Confidence intervals for the variance and difference of variances of Birnbaum-Saunders distributions
Herein, we present confidence intervals for the variance and difference of variances of Birnbaum-Saunders distributions constructed by using the bootstrap confidence interval (BCI), the generalized confidence interval (GCI), the Bayesian confidence interval (BayCI), and the highest posterior density interval (HPD). The performances of the proposed confidence intervals were investigated in terms of their coverage probabilities and average lengths by running a Monte Carlo simulation. The simulation results reveal that HPD performed the best, even for small sample sizes and/or different values of the shape parameter. To illustrate the efficacy of the proposed confidence intervals, we applied them to datasets of the PM 2.5 concentration in Chiang Mai, Thailand.
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The mean score of a sample deviates most probably from the mean score of the population, in which one is most interested. It is possible to calculate a kind of minimum and maximum value, the so called confidence interval, which indicates the position of the mean score of the population. Some worked examples elucidate the procedure of constructing such confidence intervals for the population mean, using the standard error of the (sample) mean (SEM).
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Robust confidence intervals
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This study compares and analyzes the coverage probabilities and the average interval lengths of confidence interval for a population mean based on the dependent bootstrap procedure against those based on the independent bootstrap procedure. Both dependent and independent bootstrap confidence intervals for a population mean are computed by the Bootstrap-t, Percentile, and Modified Percentile methods. Simulations show that the coverage probabilities of the dependent bootstrap confidence intervals are similar to those of the independent bootstrap confidence intervals. The average interval lengths of the dependent bootstrap method are shorter for most situations. For both the independent and dependent bootstrap confidence intervals, the coverage probabilities increase and the average interval lengths decrease as the sample size n increase for Normal, Gamma, and Chi-square distributions, as well as three methods used in this work.
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